Maths Real Numbers Medium
Show that the square of any positive integer is either of the form 4q or 4q+1 for some integer q.
Show that the square of any positive integer is either of the form or for some integer .
🔒 Step-by-step solution
Sign up free to reveal the full worked solution — hints, steps and the final answer, with a Solve-with-us walkthrough.
More questions from Real Numbers
Class 10 Maths — every question with an expert-verified, step-by-step solution.
- Q1 Express each number as a product of its prime factors: (i) 140 (…
- Q2 Find the LCM and HCF of the following pairs of integers and verify…
- Q3 Find the LCM and HCF of the following integers by applying the pr…
- Q4 Given that HCF (306, 657) = 9, find LCM (306, 657).
- Q5 Check whether 6ⁿ can end with the digit 0 for any natural number…
- Q6 Explain why 7 × 11 × 13+13 and 7 × 6 × 5 × 4 × 3 × 2 × 1+5 are comp…
- Q7 There is a circular path around a sports field. Sonia takes 18 minu…
- Q1 Prove that √5 is irrational.
- Q2 Prove that 3 + 2√5 is irrational.
- Q3 Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii…
- Q1 For some integer m, every even integer is of the form
- Q2 For some integer q, every odd integer is of the form